Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicity

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72227We consider the Jacobi matrix generated by a balanced measure of hyperbolic polynomial map. The conjecture of Bellissard says that this matrix should have an extremely strong periodicity property. We show how this conjecture is related to a certain noncommutative version of Bowen--Ruelle theory, and how the two weight Hilbert transform naturally appears in this context.Spectral TheoryMathematical Physics42B20, 42C15, 42A50, 47B35, 47B38Noncommutative Perron-Frobenius-Ruelle theorem, two weight Hilbert transform, and almost periodicitytext